I think it depends on what the medium is.

Instagram is tricky. I remember this guy that had a super passionate love affair with this cute girl that loved him. They seemed so happy and she clearly loved him.

They traveled and had an awesome sloth pet. Now I found him on a dating site and he's trying to cheat on this new girlfriend. No sign on the ex at all.

New girlfriend probably knows nothing of who the ex gf was. He deleted every picture of her. She deleted every comment or deleted herself. I don't think that's cool. These people lived for years sharing their life and it seems like a fraud for her not to have any trace of her on his profile.

If she were still there, new girlfriend could analyze wtf went on and she could predict what happened, that he cheated on that girl just like he's doing on her now. The girl was perfect.

I say, from personal experience, I would not delete myself from instagram, just close that profile and start a new one. Delete the ex or unfollow on facebook, but completely deleting each other's everything is not right. Things happened and they should stay there, pictures and all.

I guess I'm just saying this because my presence is still there on my exes profile and it sure makes me feel like I am at least given some respect. Don't pretend I never existed, that's not cool.